Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

Nan Jiang; Hoang Tran

doi:10.1515/cmam-2015-0010

Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

Nan Jiang, Hoang Tran

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which uⁿ⁺¹ + u^n-1 ≡ 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

Original language	English
Pages (from-to)	307-330
Number of pages	24
Journal	Computational Methods in Applied Mathematics
Volume	15
Issue number	3
DOIs	https://doi.org/10.1515/cmam-2015-0010
State	Published - Jul 1 2015

Keywords

CNLF
Fast-Slow Wave Splitting
NSE
Stabilization

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10.1515/cmam-2015-0010

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title = "Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems",

abstract = "In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which un+1 + un-1 ≡ 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.",

keywords = "CNLF, Fast-Slow Wave Splitting, NSE, Stabilization",

author = "Nan Jiang and Hoang Tran",

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T1 - Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

AU - Jiang, Nan

AU - Tran, Hoang

PY - 2015/7/1

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N2 - In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which un+1 + un-1 ≡ 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

AB - In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which un+1 + un-1 ≡ 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

KW - CNLF

KW - Fast-Slow Wave Splitting

KW - NSE

KW - Stabilization

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DO - 10.1515/cmam-2015-0010

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VL - 15

SP - 307

EP - 330

JO - Computational Methods in Applied Mathematics

JF - Computational Methods in Applied Mathematics

IS - 3

ER -

Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

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Keywords

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